I am not sure that there is a public API for this or anything planned (perhaps you could browse jira) but it can be done by casting to internal types.
Execution executionInA = processInstance.findActiveExecutionIn("review"); String type = ((ExecutionImpl)executionInA).getActivity().getType();
This returns the type coresponding to xml tag.
It is not the best way (by using internal classes) but it can do what you need and perhaps such functionality is on its way if not, maybe create a new request for it would be good idea.
Thanks a lot for your quick response and it works.